$1.$ A useful application of two dimensional lists in programming is to represent grid$-$like structures.

Consider the following grid of values:

$0$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$($a$)$ If we wanted to store this data in a two dimensional array, valueGrid, how would we ini$-$

tialize it so that we accessed elements in row$-$major order? $($Row major order means that

we access the row first, then the column in the row: valueGrid$[$row$][$col$]$ is the element at

$($row$,$ col$)$ in our grid.

Ex: valueGrid$[0][1]$ would be $4)$

valueGrid $=$

$($b$)$ While we normally think of grids in row major order, sometimes it is helpful to use column$-$

major order $($Column major order means that we access the column first, and then the

row; valueGrid$[$col$][$row$]$ is the element at $($row$,$ col$)$ in our grid. Ex: valueGrid$[1][0]$ would

be $4).$ How would we initialize valueGrid so that we used column$-$major order for the grid

above?

valueGrid $=$

$1$